Causes of Circular Motion Unit7.3

Forces of Circular Motion Consider a ball tied to a string that is being whirled in a horizontal circular path. Figure 7-10 Assume that the ball moves with a constant speed.

Forces of Circular Motion Because the velocity vector, v, changes direction continuously during the motion, the ball experiences a centripetal acceleration is directed toward the center of motion as described ac = vt2 r

Forces of Circular Motion The inertia of the ball tends to maintain the ball’s motion in a straight-line path; however, the string counteracts this tendency by exerting a force on the ball that makes the ball follow a circular path.

Forces of Circular Motion This force is directed along the length of the string toward the center of the circle, as shown in Figure 7-10.

Forces of Circular Motion The magnitude of this force can be found applying Newton’s second law along the radial direction. Fc = mac

Forces of Circular Motion The net force on an object directed toward the center of the object’s circular path is the force that maintains the object’s circular motion.

Forces of Circular Motion Fc = mvt2 r Force circ motion = mass x tangent speed2 distance to axis Fc = mrω2 Force circ motion = mass x distance to axis x angular speed 2

Forces of Circular Motion The force that maintains circular motion is measured in Newtons.

Forces of Circular Motion An example, the gravitational force exerted on the moon by the Earth provides the force necessary to keep the moon in orbit.

Forces of Circular Motion Because the force that maintains circular motion acts at right angles to the motion, it causes a change in the direction of the velocity. If this force vanishes, the object does not continue to move in its circular path.

Forces of Circular Motion Instead, it moves along a straight-line path tangent to the circle. To see this point, consider a ball that is attached to a string and is being whirled in a vertical circle

Motion of Rotating System To better understand the motion of a rotating system, consider a car approaching a curved exit ramp to the left at high speed.

Motion of Rotating System As the driver makes a sharp left turn, the passenger slides to the right and hits the door. At that point, the force of the door keeps the passenger from being ejected from the car.

Motion of Rotating System What causes the passenger to move toward the door? The explanation is that there must be a force that pushes the passenger outward which is sometimes called the centrifugal force.

Motion of Rotating System The phenomenon is correctly explained as follows: before the car enters the ramp, the passenger is moving in a straight- line path.

Motion of Rotating System As the car enters the ramp and travels along a curved path, the passenger, because of inertia, tends to move along the original straight-line path.

Motion of Rotating System However, if a sufficiently large force that maintains circular motion acts on the passenger, the person moves in a curved path, along with the car.

Motion of Rotating System The origin of the force that maintains the circular motion of the passenger is the force of friction between the passenger and the car seat. If this frictional force is not sufficient, the passenger slides across the seat as the car turns underneath.

Motion of Rotating System Eventually, the passenger encounters the door, which provides a large enough force to enable the passenger to follow the same curved path as the car.

Motion of Rotating System The passenger slides toward the door not because of some mysterious outward force but because the force that maintains circular motion is not great enough to enable the passenger to travel along the circular path followed by the car.

Law of Gravitational Force Note that planets move in nearly circular orbits around the sun. As mentioned earlier, the force that keeps these planets from coasting off in a straight line is a gravitational force.

Law of Gravitational Force The gravitational force is a field force that always exists between two masses, regardless of the medium that separates them.

Law of Gravitational Force It exists not just between large masses like the sun, Earth, and moon but between any two masses, regardless of size or composition. For instance, desks in a classroom have mutual attraction because of gravitational force.

Law of Gravitational Force The force between desks, however, is small relative to the force between the moon and Earth because the gravitational force is proportional to the product of the objects’ masses.

Law of Gravitational Force Gravitational force acts such that objects are always attracted to one another. Examine the illustration to the right.

Law of Gravitational Force Note that the gravitational force between Earth and the moon is attractive, and recall that Newton’s third law states that the force exerted on Earth by the moon, FmE, is equal in magnitude to and in the opposite direction of the force exerted on the Earth, FEm.

Law of Gravitational Force If masses, m1 and m2, are separated by distance r, the magnitude of the gravitational force is given by the following equation: Fg = G m1m2 r2 Gravitational force = constant x (mass 1 x mass 2) (distance btw ctr of masses)2

Law of Gravitational Force G is a universal constant called the constant of universal gravitation. It can be used to calculate gravitational forces between any two particles and has been determined experimentally. G = 6.673 x 10-11 Nm2 kg2

Law of Gravitational Force The law of universal gravitation is an example of an inverse- square law, because the force varies as the inverse square of the separation. That is, the force between two masses decreases as the masses move farther apart.